Electronic States in Quantum Hall Systems
with Internal Degrees of Freedom
Koji Muraki, Tadashi Saku, and Yoshiro Hirayama
Physical Science Laboratory
The quantum Hall (QH) effect in a two-dimensional
electron gas (2DEG) subjected to a strong
magnetic field at low temperatures is an
outstanding example of quantum phenomena
that appears in macroscopic systems. The
electronic state for each Landau-level filling
in a single-layer 2DEG is unique to the material
parameters such as the effective mass. However,
when two layers of 2DEGs are separated by
a distance of 10-20 nm in a double-quantum-well
structure, the new internal degree of freedom
associated with the layer in which the electrons
reside leads to various electronic states,
from which one can expect novel physical
properties to emerge. Furthermore, such a
system is interesting in that one can control
the interlayer tunneling and Coulomb interactions
by designing the heterostructure appropriately.
We have succeeded in fabricating a bilayer
electron system with arbitrarily tunable
densities using a double-quantum-well structure
in which the field effect of the back gate
is used in conjunction with modulation doping
[1]. Using this structure, we elucidate electronic
states specific to bilayer systems by applying
an electric field perpendicular to the layers.
Figure 1 shows the behavior of the magnetoresistance
when the electron densities of the two layers
are varied independently. The dark regions
represent the QH effect. The dashed line
shows the balance point where the electron
densities in the two layers are equal. As
the electrons are transferred from one layer
to another by the electric field (shown by
the arrow in the figure), we observe various
characteristics of the QH states. Some of
the QH states are destroyed by the electric
field, while others continue to exist. We
explain these observations in terms of level
splitting and crossing due to the electric
field (Fig. 2) [2]. According to this model,
the effect of the electric field can be understood
by analogy to the effect of a magnetic field
on atoms or molecules (the Zeeman effect).
(This work has been done in collaboration
with the group of Profs. Ezawa and Sawada,
Tohoku University.)
[1] K. Muraki et al., Jpn. J. Appl. Phys. 39 (2000) 2444.
[2] K. Muraki et al., Solid State Commun.
112 (1999) 625.
Fig. 1. Gray-scale plot of longitudinal resistance
in a constant magnetic field.
Fig. 2. Energy levels in bilayer systems
vs. level splitting due to tunneling and
electric field.
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